解法一：连通分支+DFS

第一遍DFS求出连通分支数量，并找出深度最大的结点集；第二次从中随机取出一点作为遍历起点，找出深度最大的结点集。两次结果的并集即为最终答案。

import java.io.*;
import java.util.*;
public class Main {
    private static boolean[] isVisited;
    private static int maxDepth;
    private static List<Integer> deepest;
    private static List<List<Integer>> map;
    public static void main(String[] args) throws IOException {
        StreamTokenizer in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        in.nextToken();
        int N = (int) in.nval;
        map = new ArrayList<>(N);
        for (int i = 0; i <= N; ++i) {
            map.add(new ArrayList<>());
        }
        for (int i = 1, u, v; i < N; ++i) {
            in.nextToken();
            u = (int) in.nval;
            in.nextToken();
            v = (int) in.nval;
            map.get(u).add(v);
            map.get(v).add(u);
        }
        isVisited = new boolean[N + 1];
        maxDepth = 0;
        deepest = new ArrayList<>();
        int k = 0;
        for (int i = 1; i <= N; ++i) {
            if (!isVisited[i]) {
                dfs(i, 0);
                ++k;
            }
        }
        if (k > 1) {
            out.println("Error: " + k + " components");
            out.flush();
            return;
        }
        SortedSet<Integer> ans = new TreeSet<>(deepest);
        int src = deepest.get(0);
        deepest.clear();
        Arrays.fill(isVisited, false);
        dfs(src, 0);
        ans.addAll(deepest);
        for (int i : ans) {
            out.println(i);
        }
        out.flush();
    }
    private static void dfs(int index, int deep) {
        isVisited[index] = true;
        if (deep > maxDepth) {
            maxDepth = deep;
            deepest.clear();
            deepest.add(index);
        } else if (deep == maxDepth) {
            deepest.add(index);
        }
        for (int i : map.get(index)) {
            if (!isVisited[i]) {
                dfs(i, deep + 1);
            }
        }
    }
}